Persistence pays off for Louise Southerden as she takes a dip with one of the ocean's most elusive and enigmatic creatures.

It's day three and our four-day "swimming with minke whales" trip looks like becoming a "swimming with potato cod" trip. Despite seeing plenty of marine life since starting our live-aboard adventure at Lizard Island, an hour's scenic flight north of Cairns, my 21 shipmates and I have had only teasing sightings of minkes, mainly because of the weather: every day, gale-force winds have whipped the sea into a lamington of whitecaps.

See Also

Minke whales aren't easy to spot at the best of times. They don't linger on the surface like humpbacks, their dorsal fin is the size of a bottlenose dolphin's and they don't raise their tail flukes before diving. They do, however, have a tendency to approach boats. "You don't find the whales," says our trip leader, Dr Alastair Birtles. "They find you." But not this week, not yet. Birtles, a marine biologist and senior lecturer at James Cook University, suspects the wind and waves are creating too much "white noise" for the whales to pick up the sound of our 32-metre boat, the Elizabeth EII.

He should know. Softly spoken with a David Attenborough accent, sea-blue eyes and a Santa Claus beard, he's been studying the 100 or so minke whales that frequent the northern end of the Great Barrier Reef since they were first spotted from dive boats in the 1980s.

Fieldwork on the minkes officially began in 1996, when fisherman-turned-conservationist John Rumney invited Birtles and another researcher, the late Dr Peter Arnold from the Museum of Tropical Queensland, to join live-aboard trips on his dive boat Undersea Explorer for the newly created Minke Whale Project. (Rumney's current company, Eye to Eye Marine Encounters, is now one of nine approved swim-with-minke operators; the Great Barrier Reef Marine Park Authority issued the first permits in 2003.)

It's a symbiotic relationship between tourism and science. Tourism helps fund ongoing research (there's at least one free berth for a marine biologist on every trip) and tourists assist researchers by, for instance, observing whale behaviours and contributing photos of the minkes. In return, the presence of minke whale experts enhances the tourism experience.

Every night of our trip, Birtles gives an after-dinner talk that takes us to the brink of his understanding of these "marvellous little whales", as he calls them.

"There are many basic things we still don't know about these animals," he says. "We don't know why they come or where they spend the other 10 months of the year, where and when they feed, their population size.

"It amazes me that we can be studying a new subspecies, possibly even a new species, of baleen whale in the waters of a developed country such as Australia in the 21st century, and it is quite alarming that our knowledge is so limited."

How fortunate, then, that minkes happen to be highly inquisitive. "There is no other large animal on Earth that keeps going around for hours and hours, looking at you," Birtles says. But the season is short – 90 per cent of minke whale sightings occur in June and July – so every trip counts.

We spend our first day sheltering from the high winds in one of Lizard Island's pretty coves, snorkelling and learning the code of practice for in-water minke encounters: don't touch the whales, don't swim towards a whale, don't use flash photography and stay stationary – swimmers must hold onto a rope behind the boat (a "minke line") so the whales can approach us on their own terms.

Early on the morning of day two, when the seas calm a little, we cruise east for about an hour to the southern end of Ribbon Reef 10, which forms part of the outer "barrier" of the reef. It's a known minke hot spot, though you wouldn't think so today.

All morning we stand on deck, scanning the whitecaps and finding our sea legs, before taking a break to go "extreme snorkelling". It might be rough on the surface but beneath the waves it's business as usual for gaudy parrotfish, corals of all shapes and colours, giant clams, shimmering schools of trevally, and whitetip reef sharks.

When we return to the boat, Birtles reports that he has seen two minkes, one of which lingered for an hour and three minutes (he logs every sighting on his waterproof clipboard). He cheerfully reminds us of "the P-word": patience. This is nature tourism at its most unpredictable, our itinerary determined by wind and whale sightings, hunches and educated guesses about where the whales might be, which makes the trip feel like an expedition.

On day three, two more minkes surface briefly, and disappear. That afternoon we snorkel the world-famous Cod Hole, at the northern end of Ribbon Reef 10. We swim hard against the racing current, lose sight of each other in the chop, and try not to get swept through a channel to the edge of the continental shelf and a two-kilometre drop-off.

Eventually, we surrender to the surge and let it carry us back to the boat, where we grab the "potato cod line" to watch several of these spotted 150-kilogram fish swim and swirl around us.

That night, the crew decorates the ship's bar with cardboard palm trees, a grass skirt and a cut-out sign saying "Margaritaville". Despite the party mood, disappointment lurks at the edges of our conversations. Someone makes up a knock-knock joke. Who's there? Minke. Minke who? You know, minke whale. No, sorry, I've never seen one. We imagine Joni Mitchell singing Big Yellow Minke, and Dolly Parton musing on minkes in the stream.

"Bugger the minkes," says Hazel from Hobart. "I'm going to Tonga to swim with the humpbacks." While we sleep, the boat steams south to our last chance, Lighthouse Bommie, where Birtles saw minkes on every dive last year. The next morning there are patches of blue sky, the wind has eased and the chef lifts our last-day spirits with blueberry pancakes.

We're putting on our wetsuits for another snorkel session when we hear a shout from the top deck: "Minke!" When it dives and is gone, we stick to plan A and swim over to the bommie, a 15-metre column of coral, to snorkel with turtles and an olive sea snake. Half an hour later, there is another shout. The minke has returned, and brought friends. It's on. We hurry back to the boat, grab on to the minke line and stare into the deep.

Within minutes, a shape materialises and, in what feels like a red-carpet moment, a minke whale swims along the line, as if greeting each of us in turn. Another follows. I count eight minkes at once. There's a revolving door of minkes below us and around us, swimming past, circling the boat and coming past again, closer each time. One does a pirouette on its tail. Another pokes its pointy snout (part of its name, acutorostrata, means "sharp nose") out of the water right beside me.

They're like stretch-limo dolphins, and they're not: this is less frenetic than swimming with dolphins, more ethereal. Minkes are all grace and mystery.

For almost nine hours, with a short break when we lean over the ship's railings to watch the minkes from above, we swim with 16 wild minke whales, reluctantly leaving the water only when the light begins to fade.

As soon as we clamber back onto the boat, the minke line is pulled in and the engine started – it'll take us from sunset to sunrise to cruise south to Port Douglas, where our trip will end the next morning.

But no one is in a hurry to warm up with a hot shower. Instead, we stand on deck in our wetsuits and towels watching the minkes farewell us by swimming back and forth across our wake.

The ship's dining room is abuzz that night, but we quieten down for Birtles' end-of-trip briefing. The second-roughest trip he has done in 17 years, he says, has yielded the best encounter of the season, in terms of duration and the number of whales seen.

In his most professorial voice, he gives us "11 out of 10 for persistence" and makes us all honorary Friends of the Minke Whale Project – a happy ending to a trip that had already ended happily with our all-day minke encounter. It's win-win-win, really, for us, for science and for the wild marine mammals this tourism-funded research is helping to understand and protect: the enigmatic minke whales.

FAST FACTS

Getting there Virgin Australia and Qantas fly daily to Cairns. Minke whale trips depart from Cairns, Lizard Island (aone-hour flight north of Cairns) and Cooktown (five hours from Cairns by four-wheel-drive bus through Daintree National Park).

Swimming there Eye to Eye Marine Encounters runs four-, five- and six-day live-aboard minke whale trips on the northern Great Barrier Reef every June and July, from $2900 a person plus wetsuit hire ($10 a day) and an environmental management fee ($16.50a person) collected by the Great Barrier Reef Marine Park Authority. Book well in advance; there are only five scheduled departures a season. Eye to Eye also runs private, family and group charters. See marineencounters.com.au.